Question

Find the cost of laying grass in a triangular field of sides 50m, 65m and 65m at the rate of Rs.7 per $m^2$.

[3 marks]

Answer 1

Given, ABC is a triangular field with sides
AB = a = 50m, BC = b = 65m and CA = c = 65m.

$\therefore$ Semi-perimeter of triangular field,
$s=\frac{a+b+c}{2}$
$=\frac{50+65+65}{2}=\frac{180}{2}=90m$ (0.5 marks)

$\therefore$ Area of a triangle field
$=\sqrt{s(s-a)(s-b)(s-c)}$ [by Heron’s formula] ( 0.5 marks)

$=\sqrt{90(90-50)(90-65)(90-65)}$
$=\sqrt{90\times 40\times 25\times 25}$
$=3\times 2\times 10\times 25$
$=6\times 250=1500m^2$ ( 1 mark)

The cost of laying grass per 1 $m^2$ = Rs.7
$\therefore$ The cost of laying grass per 1500 $m^2$ = 7 $\times$ 1500 = Rs.10500 ( 1 marks)

Hence, the cost of laying grass in the triangular field is Rs.10500.